Publications related to Runge's phenomenon

MATHICSE Technical Report: THU-Splines - Highly Localized Refinement on Smooth Unstructured Splines

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local h-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is taken as the input co ...

MATHICSE2021

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

Daniel Kressner, Francesco Statti, Kathrin Beatrice Glau

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. ...

2020

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

IEEE2019

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

2019

Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction

Jan Sickmann Hesthaven, Fabian Mönkeberg

To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second or ...

EDP Sciences2019

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

High-order numerical solvers for conservation laws suer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amount ...

MATHICSE2019

Runge's phenomenon

MATHICSE Technical Report: THU-Splines - Highly Localized Refinement on Smooth Unstructured Splines

Functional Tucker Approximation Using Chebyshev Interpolation

Dictionary Learning for Two-Dimensional Kendall Shapes

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

Fourier interpolation on the real line

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Graph Chatbot

Chat with Graph Search

MATHICSE Technical Report: THU-Splines - Highly Localized Refinement on Smooth Unstructured Splines

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Dictionary Learning for Two-Dimensional Kendall Shapes

Functional Tucker Approximation Using Chebyshev Interpolation

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Fourier interpolation on the real line

Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction